1. Field of the Invention
The present invention relates to an error correcting method and device, and more particularly, to an error correcting method and device for rapidly and stably correcting a triple-error/six-erasure.
2. Description of the Related Arts
U.S. Pat. No. 4,142,174 issued Feb. 27, 1979 to Chen et. al. and entitled HIGH SPEED DECODING OF REED-SOLOMON CODES, describes how to obtain the coefficients of an error location polynomial equation when locating bit errors in codeword having a double-error, triple-error, or six-error. To find the coefficients, simultaneous equations can be solved using a classical method, such as, the Berlekamp-Messay method or a Newton identity. For example, a double-error has an error location polynomial .sigma.(x) given in Equation 1. EQU .sigma.(x)=x.sup.2 +.sigma..sub.1 .multidot.x+.theta..sub.2 Equation 1
The coefficients .sigma..sub.1 and .sigma..sub.2 of error location polynomial .sigma.(x) are determined from syndromes S.sub.0 to S.sub.3 obtained from an error correction code. In particular, simultaneous Equations 2, which contain coefficients .sigma..sub.1 and .sigma..sub.2 and syndromes S.sub.1 to S.sub.3, can be solved for coefficients .sigma..sub.1, and .sigma..sub.2 using a determinant of order 2 derived from a Newton identity. ##EQU1##
Triple-error correction is more complex that double-error correction. An error location polynomial .sigma.(x) for triple-error correction is given as EQU .sigma.(x)=x.sup.3 +.sigma..sub.1 .multidot.x.sup.2 +x.sub.2 .multidot.x+.sigma..sub.3 Equation 3
or EQU .sigma.(x)=(x+.sigma..sup.i).multidot.(x+.sigma..sup.j).cndot.(x+.sigma..su p.k)=x.sup.3 +.sigma..sub.1 x.sup.2 +.sigma..sub.2 x+.sigma..sub.3 Equation 4
The coefficients .sigma..sub.1, .sigma..sub.2 and .sigma..sub.3 of the error location polynomial .sigma.(x) in Equation 3 are derivable from matrix Equation 5 and syndromes S.sub.0 to S.sub.5 from a received codeword. ##EQU2## Equation 5 has solutions shown in Equations 6. ##EQU3##
A known technology can determine the number of errors. For example, the number of errors can be obtained using methods disclosed in Korea Patent Publications No. 94-4980, 95-34202, and 96-11689. However, known methods for solving an error number decision equation can require too much operation time. For example, Korea Patent Publication No. 96-11689 uses the values of the coefficients .sigma..sub.1 and .sigma..sub.2 obtained for the double-error correction to reduce the number of operations required when obtaining the values of the coefficients .sigma..sub.1, .sigma..sub.2, and .sigma..sub.3 for triple-error correction and uses the values of the coefficients .sigma..sub.1, .sigma..sub.2, and .sigma..sub.3 when obtaining the values of coefficients .sigma..sub.1, .sigma..sub.2, .sigma..sub.3, and .sigma..sub.4 for 4-error correction. However, this method still requires complicated operations to obtain the coefficients .sigma..sub.1, and .sigma..sub.2 of a location polynomial.
In a compact disk player (CDP) or a digital audio tape (DAT) which simply error-correction-encodes and decodes source digital audio data, high quality audio data can be provided to a user by carrying out the error correction of only a double-error correction/4- or 6-erasure correction and then interpolating uncorrected data. However, in a digital compact cassette (DCC), a mini disk (MD), or a video compact disk (VCD), which employs an audio/video data compression algorithm, compressed data is frequently frequency domain data rather than time domain data, and an uncorrected error significantly degrades the quality of decoded audio or video. Thus, the DCC, MD, and VCD need better error correction capabilities and typically perform a triple-error correction to decrease uncorrected errors.
On the other hand, an error correction decoding in a conventional CD-ROM or DVD-ROM system may reduce a transmission speed of a reproduced data to a host, which will be described with reference to FIG. 1. FIG. 1 is a simplified block diagram of the CD-ROM or DVD-ROM system. The system has a disk 10, a compact disk player-digital signal processor (CDP-DSP) or DVD decoder 12, a CD-ROM decoder or a DVD-ROM host interface (I/F) 14, and an audio/video (A/V) decoder 16. Also, CD-ROM decoder or a DVD-ROM host I/F 14 is interfaced with an external host 18. When CDP-DSP or DVD decoder 12 of FIG. 1 transmits data read from disk 10 to CD-ROM decoder or the DVD-ROM host I/F 14, or A/V decoder 16, data buffering or data transmission by CDP-DSP or DVD decoder 12 is performed at high speed. However, the data or error correction decoding in CD-ROM decoder or the DVD-ROM host I/F 14 requires time and may reduce the data transmission speed. Accordingly, fast error correction decoding methods and decoders are desired.